std::ranges::push_heap() algorithm
- od C++20
- Simplified
- Detailed
// (1)
constexpr I
push_heap( I first, S last, Comp comp = {}, Proj proj = {} );
// (2)
constexpr ranges::borrowed_iterator_t<R>
push_heap( R&& r, Comp comp = {}, Proj proj = {} );
The type of arguments are generic and have the following constraints:
I
-std::random_access_iterator
S
-std::sentinel_for<I>
R
-std::ranges::random_access_range
Comp
- (none)Proj
- (none)
The Proj
and Comp
template arguments have the following default types: std::identity
, ranges::less
for all overloads.
Additionally, each overload has the following constraints:
- (1) -
std::sortable<I, Comp, Proj>
- (2) -
std::sortable<ranges::iterator_t<R>, Comp, Proj>
// (1)
template<
std::random_access_iterator I,
std::sentinel_for<I> S,
class Comp = ranges::less,
class Proj = std::identity
>
requires std::sortable<I, Comp, Proj>
constexpr I
push_heap( I first, S last, Comp comp = {}, Proj proj = {} );
// (2)
template<
ranges::random_access_range R,
class Comp = ranges::less,
class Proj = std::identity
>
requires std::sortable<ranges::iterator_t<R>, Comp, Proj>
constexpr ranges::borrowed_iterator_t<R>
push_heap( R&& r, Comp comp = {}, Proj proj = {} );
Inserts the element at the position last - 1
into the max heap defined by the range [first
; last - 1
).
-
(1) Elements are compared using the given binary comparison function
comp
and projection objectproj
. -
(2) Same as (1), but uses
r
as the source range, as if usingranges::begin(r)
asfirst
andranges::end(r)
aslast
.
The function-like entities described on this page are niebloids.
Parameters
first last | The range of elements defining the heap to push to. |
r | The range of elements defining the heap to push to. |
pred | Predicate to apply to the projected elements. |
proj | The projection to apply to the elements. |
Return value
An iterator equal to last
.
Complexity
Given N
as ranges::distance(first, last)
:
At most log(N) comparisons and 2 * log(N) projections.
Exceptions
(none)
Possible implementation
push_heap(1) and push_heap(2)
struct push_heap_fn
{
template<std::random_access_iterator I, std::sentinel_for<I> S,
class Comp = ranges::less, class Proj = std::identity>
requires std::sortable<I, Comp, Proj>
constexpr I
operator()(I first, S last, Comp comp = {}, Proj proj = {}) const
{
const auto n {ranges::distance(first, last)};
const auto length {n};
if (n > 1)
{
I last {first + n};
n = (n - 2) / 2;
I i {first + n};
if (std::invoke(comp, std::invoke(proj, *i), std::invoke(proj, *--last)))
{
std::iter_value_t<I> v {ranges::iter_move(last)};
do
{
*last = ranges::iter_move(i);
last = i;
if (n == 0)
break;
n = (n - 1) / 2;
i = first + n;
} while (std::invoke(comp, std::invoke(proj, *i), std::invoke(proj, v)));
*last = std::move(v);
}
}
return first + length;
}
template<ranges::random_access_range R, class Comp = ranges::less,
class Proj = std::identity>
requires std::sortable<ranges::iterator_t<R>, Comp, Proj>
constexpr ranges::borrowed_iterator_t<R>
operator()(R&& r, Comp comp = {}, Proj proj = {}) const
{
return (*this)(ranges::begin(r), ranges::end(r), std::move(comp), std::move(proj));
}
};
inline constexpr push_heap_fn push_heap {};
Notes
A max heap is a range of elements [f
; l
), arranged with respect to comparator comp
and projection proj
, that has the following properties:
- Given
N
asl - f
,p = f[(i - 1) / 2]
, andq = f[i]
, for all0 < i < N
, the expressionstd::invoke(comp, std::invoke(proj, p), std::invoke(proj, q))
evaluates tofalse
. - A new element can be added using
ranges::push_heap
, in O(log(N)) time. - The first element can be removed using
ranges::pop_heap
, in O(log(N)) time.
Examples
#include <algorithm>
#include <cmath>
#include <iostream>
#include <vector>
void out(const auto& what, int n = 1)
{
while (n-- > 0)
std::cout << what;
}
void print(auto rem, auto const& v)
{
out(rem);
for (auto e : v)
out(e), out(' ');
out('\n');
}
void draw_heap(auto const& v);
int main()
{
std::vector<int> v {1, 6, 1, 8, 0, 3,};
print("source vector v: ", v);
std::ranges::make_heap(v);
print("after make_heap: ", v);
draw_heap(v);
v.push_back(9);
print("before push_heap: ", v);
draw_heap(v);
std::ranges::push_heap(v);
print("after push_heap: ", v);
draw_heap(v);
}
void draw_heap(auto const& v)
{
auto bails = [](int n, int w)
{
auto b = [](int w) { out("┌"), out("─", w), out("┴"), out("─", w), out("┐"); };
if (!(n /= 2))
return;
for (out(' ', w); n-- > 0; )
b(w), out(' ', w + w + 1);
out('\n');
};
auto data = [](int n, int w, auto& first, auto last)
{
for (out(' ', w); n-- > 0 && first != last; ++first)
out(*first), out(' ', w + w + 1);
out('\n');
};
auto tier = [&](int t, int m, auto& first, auto last)
{
const int n {1 << t};
const int w {(1 << (m - t - 1)) - 1};
bails(n, w), data(n, w, first, last);
};
const int m {static_cast<int>(std::ceil(std::log2(1 + v.size())))};
auto first {v.cbegin()};
for (int i {}; i != m; ++i)
tier(i, m, first, v.cend());
}
source vector v: 1 6 1 8 0 3
after make_heap: 8 6 3 1 0 1
8
┌─┴─┐
6 3
┌┴┐ ┌┴┐
1 0 1
before push_heap: 8 6 3 1 0 1 9
8
┌─┴─┐
6 3
┌┴┐ ┌┴┐
1 0 1 9
after push_heap: 9 6 8 1 0 1 3
9
┌─┴─┐
6 8
┌┴┐ ┌┴┐
1 0 1 3
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